Sparsity-induced identification of factor-augmented VAR models

The factor-augmented vector autoregressive (FAVAR) model, first proposed by Bernanke, Bovin, and Eliasz (2005, QJE), is now widely used in macroeconomics and finance. In this model, observable and unobservable factors jointly follow a vector autoregressive process, which further drives the comovement of a large number of observable variables. We study the identification restrictions in the presence of observable factors. We propose a likelihood-based two-step method to estimate the FAVAR model that explicitly accounts for factors being partially observed. We then provide an inferential theory for the estimated factors, factor loadings and the dynamic parameters in the VAR process. We show how and why the limiting distributions are different from the existing results.

We introduce a time-varying (TV) factor-augmented vector autoregressive (FAVAR) model to capture the TV behavior in the factor loadings and the VAR coefficients. To consistently estimate the TV parameters, we first obtain the unobserved common factors via the local principal component analysis (PCA) and then estimate the TV-FAVAR model via a local smoothing approach. The limiting distribution of the proposed estimators is established. To gauge possible sources of TV features in the FAVAR model, we propose three L 2 -distance-based test statistics and study their asymptotic properties under the null and local alternatives. Simulation studies demonstrate the excellent finite sample performance of the proposed estimators and tests. In an empirical application to the U.S. macroeconomic dataset, we document overwhelming evidence of structural changes in the FAVAR model and show that the TV-FAVAR model outperforms the conventional time-invariant FAVAR model in predicting certain key macroeconomic series.

ABSTRACTGDP forecasting remains a challenge for a small open developing economy. Faced with insufficient and low-frequency data, central bank forecasters cannot project GDP reliably for the purpose of monetary policy decision-making. An attempt is made to forecast GDP using a factor-augmented vector autoregressive (FAVAR) model for a small open developing economy. The forecasting accuracy of the FAVAR model is examined through sequential forecasts and benchmarked against a Bayesian vector autoregressive (BVAR) model. The main finding of this study is that a FAVAR model can generate consistent GDP projections for a small open developing economy despite data inadequacy.

Vector autoregressive (VAR) models are among the most widely used econometric tools in the fields of macroeconomics and financial economics. Much of what we know about the response of the economy to macroeconomic shocks and about how various shocks have contributed to the evolution of macroeconomic and financial aggregates is based on VAR models. VAR models also have been used successfully for economic and business forecasting, for modeling risk and volatility, and for the construction of forecast scenarios. Since the introduction of VAR models by C.A. Sims in 1980, the VAR methodology has continuously evolved. Even today important extensions and reinterpretations of the VAR framework are being developed. Examples include VAR models for mixed-frequency data, VAR models as approximations to DSGE models, factor-augmented VAR models, new tools for the identification of structural shocks in VAR models, panel VAR approaches, and time-varying parameter VAR models. This volume collects contributions from some of the leading VAR experts in the world on VAR methods and applications. Each paper highlights and synthesizes a new development in this literature in a way that is accessible to practitioners, to graduate students, and to readers in other fields

We consider a set of minimal identification conditions for dynamic factor models. These conditions have economic interpretations, and require fewer number of restrictions than when putting in a static-factor form. Under these restrictions, a standard structural vector autoregression (SVAR) with or without measurement errors can be embedded into a dynamic factor model. More generally, we also consider overidentification restrictions to achieve efficiency. General linear restrictions, either in the form of known factor loadings or cross-equation restrictions, are considered. We further consider serially correlated idiosyncratic errors with heterogeneous coefficients. A numerically stable Bayesian algorithm for the dynamic factor model with general parameter restrictions is constructed for estimation and inference. A square-root form of Kalman filter is shown to improve robustness and accuracy when sampling the latent factors. Confidence intervals (bands) for the parameters of interest such as impulse responses are readily computed. Similar identification conditions are also exploited for multi-level factor models, and they allow us to study the spill-over effects of the shocks arising from one group to another.

Environmental policy in the European Union is a frequent topic when speaking about a strategic development of national economies, their sectors, or companies. This paper is focused on transmissions between the European carbon market and the Czech steel industry. This relationship is worth exploring for two main reasons – first, iron and steel industry is responsible for a substantial part of CO2 pollution covered by the European Union emissions trading system (EU ETS) and, second, this sector is a traditional and vital industry in the Czech Republic. We use the dynamic Factor Augmented Vector Autoregression (FAVAR) model and Granger causality analysis to identify and assess the interactions between the factors of the EU ETS (prices of emission allowances and grandfathering), and factors of the steel industry like prices and amounts of production. To the best of our knowledge, this is the first application of the FAVAR model to analyse an industrial sector, and it is also the first analysis of the given topic where so many influencing factors are involved (this is allowed by the FAVAR model). The main results show that steel companies in the Czech Republic pass through the emission costs to customers.

This paper uses 39 monthly time series of the financial market observed from January 2000 to April 2017 to estimate a financial conditions index (FCI) for South Africa. The empirical technique used is a dynamic factor model with time-varying factor loadings proposed by Koop and Korobilis (Eur Econ Rev 71(C):101–116, 2014) based on the principal component analysis and the Kalman smoother. In addition, we estimate a time-varying parameter factor-augmented vector autoregressive (TVP-FAVAR) model, which includes, in addition to the FCI, two observed macroeconomic variables. The results show the ability of the estimated FCI to predict risks in the financial market emanating from both the domestic market and the global market. Furthermore, the TVP-FAVAR model outperforms the constant-loading factor-augmented vector autoregressive model and the traditional vector autoregressive model in the out-of-sample forecasting of the inflation rate and the real gross domestic product growth rate. Finally, tighter financial conditions contract the real economy and are deflationary at the same time. Importantly, the responses of macroeconomic variables are asymmetric and vary over time.

Since the mid-1970s, a number of studies have used vector autoregressive (VAR) models to evaluate the magnitude and timing of macroeconomic impacts on agriculture. Use of the VAR method has been viewed as a way to obtain empirical evidence about these impacts that might not emerge from more traditional overidentified and less dynamic econometric models. The hope has been that by placing minimal restrictions on VAR models, the true structure of the economic relationships under investigation can be observed. While the aim is laudable, critics of VAR models have argued that it has had the unfortunate consequence of obscuring some important structural identification issues and seeming to promise that something can be obtained for nothing (Cooley and Leroy, Leamer). They point out that identifying restrictions are required to give economically interpretable meaning to the results of any simultaneous equation model (SEM). In standard practice, identification of VAR models is obtained implicitly by choice of a Choleski decomposition of the covariance matrix of one-step-ahead forecast errors, which is equivalent to imposing a recursive structure for the economy. Of concern is that the recursive structure may not be believable. Further, as Bernanke has observed, examination of ad hoc variants of the recursive order implies a strange set of prior beliefs in which the analyst holds strongly that the system is recursive but is not sure in what order the variables should be arranged. In response to these concerns, several recent papers have pointed out that identification of VAR models does not have to rely on the assumption that the contemporaneous structure is recursive (Bernanke, Sims). Rather, the distinguishing features of a VAR model are, first, that identification rests on the assumption that distinct, mutually orthogonal behavior shocks drive the economy, and, second, that lagged relationships among the endogenous and exogenous variables (if any) are left entirely unrestricted. Given these features, a VAR model must be identified solely by restrictions placed on the contemporaneous interactions among the variables, but the identifying restrictions do not have to preclude simultaneity. In this paper, we elaborate on the structural interpretation of VAR models and use this analysis to examine monetary impacts on agricultural prices. We discuss the identification problem and the implications of a recursive structure. We illustrate our points with respect to the three-variable model of money, industrial prices, and agricultural prices that has been used in several articles to evaluate the effects of monetary shocks on price dynamics (Bessler, Devadoss and Meyers). We then introduce a somewhat richer behavioral model of the macroeconomy and its effects. A simultaneous model is shown to offer a more believable identification of monetary policy and other macroeconomic shocks than a recursive model, and monetary impacts on agricultural prices are assessed.

This paper examines the effects of monetary policy on macroeconomic variables in Pakistan’s economy using a data-rich environment. We used the factor-augmented vector autoregressive (FAVAR) methodology, which contains 115 monthly variables for the period 1992:01 to 2010:12. We compared the results of VAR and FAVAR model and the results showed that FAVAR model explains the effects of monetary policy which are consistent with the theory and better than the VAR model. VAR model shows the existence of price puzzle and liquidity puzzle in Pakistan while FAVAR model did not provide any evidence of puzzles. Interest rate negatively influences prices, hence interest rate is a good instrument for controlling inflation in Pakistan but it takes a lag of 5 months. The transmission of monetary policy shock is faster in case of prices as compared to output in Pakistan. FAVAR model supports the effectiveness of interest rate channel in Pakistan.

Extracting information from high-dimensional time series in the form of underlying factors is an increasingly popular methodology in forecasting applications. In this paper, principal component analysis (PCA) and three other methods for factor extraction are compared based on their deterministic and probabilistic forecasting performances using factor-augmented vector autoregressive (FAVAR) models. The existing PCA-based methods use only the contemporaneous covariance matrix of the data, while the other methods rely on weighted lagged cross-covariance matrices. Our empirical study considers four crude oil future price instruments and a 241 variable dataset of global energy prices and quantity, macroeconomic indicators, and financial series which are thought to influence oil price movements. Overall empirical findings are: (1) the PCA-based method performs better at shorter forecast horizons whereas the new methods involving lagged cross-covariance matrices tend to perform better at longer horizons (2 months or greater); (2) the performance ranking of the four methods under both deterministic and probabilistic forecasting is greatly affected by the number of factors included in the FAVAR models; (3) the forecast performances of the four methods are close to each other and no method performs uniformly better than the others. More research on the role of temporal dependence in determining the number of factors is warranted.

<p>MODELING AZERBAIJAN’S INFLATION AND OUTPUT <span>USING A FACTOR-AUGMENTED VECTOR </span><span>AUTOREGRESSIVE (FAVAR) MODEL</span></p>

Commodity index trading in futures markets is a relatively new investment strategy whose consequences are not fully understood. This paper tests the hypothesis that long-only, passive index trading in agricultural futures markets influences futures prices. Vector Autoregressive (VAR) models are a common empirical research approach for analyzing index trading. Factor-Augmented Vector Autoregression (FAVAR) models are a new approach to analyzing index trading. FAVAR models can incorporate a large data set into the traditional VAR framework. Using a FAVAR model improves the analysis by including additional market factors relevant to futures price formation. Models were estimated for 13 agricultural commodities (corn, soybean, soybean oil, soybean meal, soft red winter wheat, hard red winter wheat, cotton, cocoa, sugar, coffee, live cattle, feeder cattle, and lean hog) from January 2006 to December 2022. The results demonstrate the added value of FAVAR models in explaining the dynamics between prices and index trading. The conclusions are similar to other findings that prices lead index positions; however, adding demand-related data through a FAVAR model allows for a better understanding of market dynamics.

This paper proposes an effective statistical based vibration health monitoring technique using Auto Regressive (AR) parameters and Support Vector Machine (SVM) for truss type structures. The finite element method has been utilized to obtain acceleration response signals of a space truss structure under random excitations. The signals are then processed to extract their AR parameters as the feature vectors in which the AR parameters of the healthy structure are considered to be the reference baseline data. A Damage Index is then defined to be the standard deviation of the feature vectors from the baseline data. The proposed index provides an effective tool to detect the damage in the structure. It is shown that using only one sensor, it is still possible to accurately detect the damage. To locate the damage, data classification technique based on Support Vector Machine (SVM) has been employed. It is shown that SVM can successfully classify different signals extracted from the structure. Finally extensive sensitivity analysis has been performed to study the effect of different parameter such as crack size, number of sensors and AR parameter numbers on the accuracy of detection and localization processes.

Purpose This study examines the impact of macroeconomic shocks on the formal labor market in Brazil, segmented by workers’ education levels. Design/methodology/approach We estimate a factor-augmented vector autoregression (FAVAR) model identified via heteroskedasticity based on the two-step method of Bernanke et al. (2005), along with the identification approach proposed by Brunnermeier et al. (2021). Findings Various types of macroeconomic shocks, such as those related to monetary policy and expectations, are identified. Our empirical results support the theory of heterogeneous agents for the Brazilian formal labor market over the business cycle, showing that the impacts of these shocks on more educated workers were smaller than other groups. Additionally, the findings suggest that the primary adjustment mechanism of firms is through hiring rather than separations and reveal a pro-cyclical pattern in turnover. Originality/value Unlike previous studies, this paper applies a FAVAR model identified via heteroskedasticity to analyze the effects of macroeconomic shocks on the formal labor market in Brazil, offering additional evidence on how these effects vary across workers with different education levels.

Longevity risk is putting more and more financial pressure on governments and pension plans worldwide due to pensioners’ increasing trend of life expectancy and the growing numbers of people reaching retirement age. Lee and Carter (1992, Journal of the American Statistical Association, 87(419), 659–671.) applied a one-factor dynamic factor model to forecast the trend of mortality improvement, and the model has since become the field’s workhorse. It is, however, well known that their model is subject to the limitation of overlooking cross-dependence between different age groups. We introduce Factor-Augmented Vector Autoregressive (FAVAR) models to the mortality modelling literature. The model, obtained by adding an unobserved factor process to a Vector Autoregressive (VAR) process, nests VAR and Lee–Carter models as special cases and inherits both frameworks’ advantages. A Bayesian estimation approach, adapted from the Minnesota prior, is proposed. The empirical application to the US and French mortality data demonstrates our proposed method’s efficacy in both in-sample and out-of-sample performance.